Answer
$\frac{27}{2}+\frac{27\sqrt 3}{2}i$
Work Step by Step
Use the given conditions, we have:
$[3(cos20^\circ+i\ sin20^\circ)]^3=3^3(cos(3\times20)^\circ+i\ sin(3\times20)^\circ)=27(cos60^\circ+i\ sin60^\circ)=27(\frac{1}{2}+\frac{\sqrt 3}{2}i)=\frac{27}{2}+\frac{27\sqrt 3}{2}i$
